instabilities of electrically forced jets moses hohman (univ. of chicago thoughtworks) michael shin...
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Instabilities of Electrically Forced Jets
Moses Hohman (Univ. of Chicago Thoughtworks)
Michael Shin (Materials Science, MIT)
Greg Rutledge (Chemical Engineering, MIT)
I hate Computers
David QuereIMA WorkshopJanuary, 2001
Electrospinning is complicated
Electrohydrodynamics, evaporation, rheology, air drag, electrostaticswetting, solid-liquid charge transfer, temperature gradients, etc.
Which factors influence the final product?
The Product:
The Physics:
Approaches:
(1) Experimental: Try to control various processes, in hope thatsomething jumps out.
(2) Numerical simulations. Include all physical factors and try to understand which dominate.
(3) “Theory”. Understand a single effect quantitatively. Do not “curve fit” results to experiments but instead try to assess how much of the physics stems from this effect.
Caveats:Free parameters are absolutely unacceptable.
Numerical simulations of parts of the system always necessary.
A principle advantage of “theory” as opposed to numerical simulations and experiments is that
one also studies what does not happen.
I. Procedure for calculating instability thresholds (flavor)
II. Difficulties
III. Applications. Electrospinning, etc.
“Strange” effects in Fluid Conductors:
(1) Surface Charge Density + Tangential Electric field
Tangential Electrical Stress.
In a fluid, this must be balanced by viscous stress (flow).
Both viscosity and conductivity are singular parameters.
(2) A Non-Ohmic mechanism for conduction:
G.I. Taylor, 1964 (78 years old)
h
QEKhI 22
h(z)K
Stability of a thinning Jet:.
(1) Locally jet is a cylinder (constant radius h, surface charge
Find h
(2) Find global shape:
(h(z),z),E(z))
(3) Piece together stability properties along the jet
Previous Work on Linear Stability of uncharged cylinders
(Mestel JFM 1994,1996)
K 0 1
0
1
Nayyar andMurty, 1960
Saville (1970)
Saville (1972)Saville (1972) Saville (1970)
Nayyar andMurty, 1960
Saville (1972)
Nayyar andMurty, 1960
Experiments: Must Include Surface Charge
Experiments
Electrostatics
+
+
-
-
E
Line Dipole + Line Charge
P(z) (z)dielectric dielectric
free charge D free charge
Long wavelength Instabilities
varicose whipping
h
h<<
Whipping Mode: the electrostatics
3|)(|
))(()(
|)(|
)()()(
srx
srxsPds
srx
sdsxx
Field from aline charge
Field from aline dipole
E
P
determined by matching outside field to field inside the jet. (and using Gauss’ Law)
R
hhnE
hP D
022
2
2ˆ
)(2
)(
E.G:
dielectric polarization
dipolar free charge density
Whipping Mode: the fluid mechanics
centerlinetzr ),(
Kds
dTrh 2 External Forces:
Surface Tension+Electrical Stress
acceleration
Force Balance
Torque Balance
0ˆ NTtds
Md
Local Couple:Electrical Stresses
Bending Moment: viscous (Maha)
dielectric M
E
Perfect Conductor: Waves
0
)4
)(( 2
222
XEh
hXh s
++
++--
--
spring
E
++
++--
--
Finite K:Tangential Stresses Drive Whipping Instability
....4
)4
)((
222
222
2
XK
Eh
XEh
hXh
st
s
torque-producing instability
Comparison with Saville (1972)
• inviscid• K=0.7
• no charge density
10-2 10-1 100 10110-6
10-5
10-4
10-3
10-2
10-1
100
Re
k
E
There is also an unstable varicose mode.
The mechanism is not the Rayleigh instability, but is electrically driven.
Varicose
Have 2 Unstable (Electrically Driven) Modes:
Who wins at high field?
Phase Diagrams
2% solution of PEO in waterE=2 kV/cm
AI
mlQPcmSK
10
min/15,7.16,/120
-0.3
-0.2
-0.1
0
0.1
0.2
-1 -0.5 0 0.5 1 1.5 2 2.5-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
log10
( / (esu / cm 2))
log 10
(h /
cm)
Whipping
Varicose
-0.3
-0.2
-0.1
0
0.1
0.2
-1 -0.5 0 0.5 1 1.5 2 2.5-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
log10
( / (esu / cm 2))
log 10
(h /
cm)
Whipping
Varicose
Phase Diagrams
AI
mlQPcmSK
10
min/15,7.16,/120
2% solution of PEO in waterE=2 kV/cm
Phase Diagrams
Varicose
Whipping
2% solution of PEO in waterE=2 kV/cm
AI
mlQPcmSK
10
min/15,7.16,/120
I
Qh
2
Phase Diagrams
2% solution of PEO in water AI
mlQPcmSK
10
min/15,7.16,/120
Varicose
Whipping
Whipping Mode
jet
2),,(),(
Q
hEhQE
2 4 6 8 10 12 14 16 18
0.5
1
1.5
2
2.5
3
3.5
Q (ml/min)
E (
kV
/cm
)
BENDING
BENDING + VARICOSE
VARICOSE STEADY JET
Viscosity Viscosity/10
Conclusions
The procedure quantitatively capture aspects of electrospinning.
Honest comparisons with experiments allow us to hone in on subtle details.
The Ideas are fairly general. Should have applicibility to many otherProblems.